Question 6:

(DATES AND TIMES SHORT).

12/9/1496 21:37:48 2/3/6743 09:24:17

T^2 = A/B = 10^6 ms²

a. What are the whole numbers of the years, months, days, hours, minutes and seconds between the two dates and times?

b. What is the value of y?

c. What are the magnitudes of T^1, T^-1 and T^-2?

d. What are the values of t, A and B?

Answer:

a.

w = y – M/(365/31) = 6743 – 1496 – 1 = 5246

w = M – d/31 = 12 – 9 + 3 – 1 = 5

w = d – h/24 = 31 – 12 + 2 – 1 = 20

w = h – m/60 = 24 – 21 + 9 – 1 = 11

w = m – s/60 = 60 – 37 + 24 – 1 = 46

w = s – cs/100 = 60 – 48 + 17 = 29

Because there is no obvious consensus on precisely how many days are in month, that is 28 – 31, therefore, when we are using months, in order to get the months and days to match and corroborate we must state that we are using 31 days in a month, therefore, we are using conversion factor of 365/31 months in a year. However, you could use a different whole number (a number without a decimal) for the conversion factor (or the amount of days in a month) such as 365/30 = 73/6.

b.

s/60 = 29/60

m = w + s/60 = 46 + 29/60 = 2789/60

m/60 = (2789/60)/60 = 2789/3600

h = w + m/60 = 11 + 2789/3600 = 42389/3600

h/24 = (42389/3600)/24 = 42389/86400

d = w + h/24 = 20 + 42389/86400 = 1770389/86400

d/31 = (1770389/86400)/31 = 1770389/2678400

M = w + d/31 = 5 + 1770389/2678400 = 15162389/2678400

M/(365/31) = (15162389/2678400)/(365/31) = 15162389/31536000

y = w + M/(365/31) = 5246 + 15162389/31536000 = 165453018389/31536000

c.

T^1 = √(A/B) = 10^3 ms

T^-1 = √(B/A) = 10^-3 ks

T^-2 = B/A = 10^-6 ks²

d.

t = y × 31536000 = 1.65453018389 × 10^11 s

X = 1.65453018389

A = tT^1 = X × 10^11 × 10^3 = X × 10^14 ms

B = A/T^2 = X × 10^14 / 10^6 = X × 10^8 ks

Hand written example: